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Jinrui wa Suitaishimashita (Humanity has Declined) has a fantastically headstrong, snarky and cynical heroine. Its not an over the top intelligence like some of your examples, but I found her completely sensible outlook a departure from a lot of anime leads.

Well I always thought the MC was pretty good, got thrown into a dangerous situation and thrives, then the plot does a 180 and totally implodes into itself, every chance it gets, destroying any meaningful character development.

Oh well, Griffith is somewhat of a genius but I wouldn't count Berserk anyway. However, the manga is always worth a read! At least Guts himself is not too much of an idiot... not someone who dabbles with intellectuals, but not one who is left puzzled easily, either.

Hyouka. It's a really well done anime with great animation, interesting and very likable characters and the main "thing" are different mysteries with most often surprising, yet very logic solutions. It's really, really worth watching ;)

Sure. I just mean to say that intelligence is not their defining characteristic, like it would be for the main characters of Death Note. Much rather, Alucard's main characteriscs are overwhelming power and bloodlust, and Integra's her iron will. Intelligence is just in the second row of things that characterise them.

Like, but Kira and L on something and they will instantly start thinking. Put Alucard on something, and he will start killing.

no arguing with that, but OP asked for animes with intelligent main characters. That does not exclude animes with characters like hellsing/alucard that have many more, and more important(for their character) traits than their intelligence, does it?

No, he's a genius with tremendous luck, he's portrayed as a genius the entire series and called one because he is, at the same time it's said the tremendous luck he has got and that he manages to roll the games to his side all the time.

At the last game on the anime the sides are contrasted as him being the genius VS washizu the guy with god-like Luck.

Eh.... well... regardless of the main character's intellect, the world of Black Lagoon is so stupid it hurts :& Like, fantasy elements can be part of a world and that world can still be plausible in itself. But Black Lagoon plays so much with completely random elements that are just unlikely (fortunate coincidences) to make the protagonists look cooler, and then makes it look like such a thing would be plannable.

It's only worth watching for someone who can ignore all that and enjoy the action, I guess.

a lot of anime gets driven by random plot devices to keep the show going.

That it is so fucking over the top with all the action is what makes the show so good because, you get sweeped away into a world there is close enough to reality for you to believe it exist but still far enough to be a fantasy world.

Yeah, that is all true, but the general rule writers go by is that bad coincidences that happen to the protagonist are a good way to drive a story forward, while good ones appear too convenient and often implausible and usually considered poor writing. At the same time a scenario can be as unrealistic as it wishes to and deploy fantasy elements, magic, absolute weirdness... whatever. But it should be plausible in itself, in other words it needs to stick to the rules it was given.

Stories like Harry Potter or Lord of the Rings as good fantasy scenarios create their very own world, but they stick to their logics. Everything that happens fits the scenario, even the mysterious things. And you will find more unpleasant coincidences than pleasant ones in them.

you get sweeped away into a world there is close enough to reality for you to believe it exist but still far enough to be a fantasy world.

They are fantasy worlds, but they allow immersion by sticking to their own rules.

So what Black Lagoon does poorly is, that it allows too much convenient coincidence. The solution to episode one for example... it is completely RIDICULOUS. And that is the point where the immersion breaks... so, they find themself in a bad situation and need to find a way to solve it, a very normal thing for a story. But they end up doing it with something that is completely implausible. One does not need much experience with real world ballistics and physics to figure out that that is not a way of taking aim that would plausibly ever work. It is daring and risky, okay, that in itself is totally fine. But the chance for it to work, no matter the users' skills -in fact, that is probably the smallest factor of all in the equation-, is so abysmal that the solution just appears laughable.

See, I didn't have a problem with the way Black Lagoon works. It follows the same logic of pulp action, which is essentially the better you are, or the cooler you are the more successful you are at things. The more of a hero you are, or the cooler of a villain, the more the universe makes things go your way.

Like, the better you are at shooting guns also makes you less likely to be shot.

If you've ever played the RPG Spirit of the Century, or have watched or read any pulp action movies or books you might have a better idea of what I'm talking about.

Harry Potter, on the other hand, is one of my go to examples for an incredibly inconsistent fantasy world. The entire universe falls apart at the seams the instant you try to examine it in detail.